Sterling's future has been the subject of speculation for months, as the 20-year-old is yet to accept a contract offer from the Premier League outfit with two years remaining on his current deal.
Former Liverpool winger Barnes has urged the England international to put pen to paper with the Merseyclub and continue his development under Brendan Rodgers.
He told talkSPORT: "Raheem Sterling should absolutely sign the contract and stay at Liverpool,
"I would advise any young player who has just been in the game for a year or so to stay and learn his trade. Show a level of consistently over a four or five-year period before you make a big move. You will then be judged as a £50 million player.
"We've seen it with Scott Sinclair and Jack Rodwell at Manchester City. Where are they now?
"Sterling is not ready for a move to Barcelona, Real Madrid or Manchester City. He needs another two or three years at Liverpool. Then, if he decides he wants to move on, fine. He has to be very careful though.
"Sometimes the bad advice is not only the most lucrative but also sounds like the best advice.
"He’s not been playing consistently well over a number of years though. Maybe his form has suffered because of all the speculation about his future.
"For any young player, similar to Harry Kane [and Sterling], I would advise you to show a level of consistently where you're happy and people accept you.
"Then, if you want to put yourself under pressure by making a big money move, do that because it could all go wrong."
